Rivero-Castillo, Daniel; Pijeira, Héctor; Assunçao, Pedro Edge detection based on Krawtchouk polynomials. (English) Zbl 1358.94014 J. Comput. Appl. Math. 284, 244-250 (2015). Summary: Discrete orthogonal polynomials are useful tools in digital image processing to extract visual object contours in different application contexts. This paper proposes an alternative method that extends beyond classic first-order differential operators, by using the properties of Krawtchouk orthogonal polynomials to achieve a first order differential operator. Therefore, smoothing of the image with a 2-D Gaussian filter is not necessary to regularize the ill-posed nature of differentiation. Experimentally, we provide simulation results which show that the proposed method achieves good performance in comparison with commonly used algorithms. Cited in 4 Documents MSC: 94A08 Image processing (compression, reconstruction, etc.) in information and communication theory 33C47 Other special orthogonal polynomials and functions 42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis 94A11 Application of orthogonal and other special functions Keywords:image processing; edge detection; Krawtchouk polynomials; discrete orthogonal polynomials PDFBibTeX XMLCite \textit{D. Rivero-Castillo} et al., J. Comput. Appl. Math. 284, 244--250 (2015; Zbl 1358.94014) Full Text: DOI References: [1] Withey, D. J.; Pedrycz, W.; Koles, Z. J., Dynamic edge tracing: boundary identification in medical images, Comput. Vis. Image Underst., 113, 10, 1039-1052 (2009) [2] Niu, Y.; Wu, X.; Shi, G.; Wang, X., Edge-based perceptual image coding, IEEE Trans. Image Process., 21, 1899-1910 (2012) · Zbl 1373.94307 [3] Papari, G.; Petkov, N., Edge and line oriented contour detection: state of the art, Image Vis. Comput., 29, 2-3, 73-103 (2011) [4] Pratt, W. K., Digital Image Processing (2001), John Wiley & Sons: John Wiley & Sons NY [5] Solomon, C.; Breckon, T., Fundamentals of Digital Image Processing. A Practical Approach with Examples in MATLAB (2011), Wiley-Blackwell: Wiley-Blackwell Oxford [6] Chihara, T. S., An Introduction to Orthogonal Polynomials (1978), Gordon and Breach: Gordon and Breach NY · Zbl 0389.33008 [8] Baik, J.; Kriecherbauer, T.; McLaughlin, K. T.-R.; Miller, P. D., Discrete Orthogonal Polynomials: Asymptotics and Applications (2007), Princeton Univ. Press: Princeton Univ. Press Princeton, NJ · Zbl 1119.41001 [9] Nikiforov, A. F.; Suslov, S. K.; Uvarov, V. B., Classical Orthogonal Polynomials of a Discrete Variable (1991), Springer-Verlag: Springer-Verlag NY · Zbl 0743.33001 [10] Beals, R.; Wong, R., Special Functions (2010), Cambridge Univ. Press: Cambridge Univ. Press Cambridge [11] Mathews, J. H.; Fink, K. K., Numerical Methods Using MATLAB (1999), Prentice-Hall Inc.: Prentice-Hall Inc. Upper Saddle River, NJ [12] Rice, J. R., The Approximation of Functions, Vol. 2: Nonlinear and Multivariate Theory (1969), Addison-Wesley Publ. Co.: Addison-Wesley Publ. Co. Reading, Mass. · Zbl 0185.30601 [13] Hoggar, S. G., Mathematics of Digital Images (2006), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 1112.68128 [14] Krishnamoorthi, R.; Sathiya Devi, S., Image retrieval using edge based shape similarity with multiresolution enhanced orthogonal polynomials model, Digit. Signal Process., 23, 555-568 (2013) [15] Lopez-Molina, C.; De Baets, B.; Bustince, H., Quantitative error measures for edge detection, Pattern Recognit., 46, 4, 1125-1139 (2013) [16] Torre, J. V.; Poggio, T. A., On edge detection, IEEE Trans. Pattern Anal. Mach. Intell., PAMI-8, 147-163 (1986) [17] Lopez-Molina, C.; De Baets, B.; Bustince, H.; Sanz, J.; Barrenechea, E., Multiscale edge detection based on Gaussian smoothing and edge tracking, Knowl.-Based Syst., 44, 0, 101-111 (2013) [18] Bhattacharyya, P.; Ganesan, L., An orthogonal polynomials based frame work for edge detection in 2D monochrome images, Pattern Recognit. Lett., 18, 319-333 (1997) [19] Haralick, R. M., Digital step edges from zero crossing of second directional derivatives, IEEE Trans. Pattern Anal. Mach. Intell., 6, 58-68 (1984) [20] Onural, L., 3D Video Technologies: An Overview of Research Trends (2011), SPIE Press: SPIE Press Washington This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.